Are these sentences correct?
- This book really resonates with me.
- I really resonate with this book.
Also, are there any differences in meaning?
Short answer, yes -- at least, the first one. The second one seems off, though. That is to say, it's grammatically correct, but I don't think it has the meaning that you expect.
In the first one, "this book really resonates with me," the conveyed meaning would be something along the lines of, "there's something about this book that I feel like I can identify with," or, "I can really empathize with this book's meaning."
In the second one, "I really resonate with this book," the above meaning isn't there, and frankly it sounds bizarre -- but I couldn't tell you why exactly. It might be because the original meaning of "resonate" is to emit sound like a bell does, or to amplify a sound -- usually a single note or chord. In such a context, one could say, "the cathedral resonated with the music from the pipe organ." In that sense, a person doesn't resonate; only objects. I think that in general, a good rule for use would be that (inanimate object/idea) resonates with (person/group).
(Plus it has more technical meanings in electronics and radio wave theory, but that's unrelated here.)
There is an inherent poetry to the expression; both forms of the expression make poetic sense. When I seem to find myself within the pages of a book, the book seems to "resonate with me." If I have empathy with the characters, if their experiences fill me with associations from my own life, then the "sound" made by the book is "reverberating" within me. I am resonating with the book. I have become that cathedral.